Rule of Product

The rule of product, also sometimes called the product rule principle or multiplication principle, is a basic counting principle in combinatronics. It states that if we have an event A followed by a second event B whose outcome is independent of event A, and event A can occur in m ways and event B can occur in n ways, then there are m * n possible ways for the pair of events to occur. This rule can be extended to three or more events.

In the terms of set theory, the rule of product tells us that the cardinality of set A multiplied by the cardinality of set B is equal to the cardinality of the cross product of A and B:

|A| * |B| = |A \times B|


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